The lead prosecutor briefed the judge on the talks in an effort to fend off a claim that members of Congress had unlawfully meddled in the negotiations.Prosecutors and defense lawyers are still negotiating toward a plea agreement for the men accused of plotting the Sept. 11, 2001, attacks despite the Biden administration’s refusal to endorse certain proposed conditions, the lead prosecutor said in court on Wednesday at Guantánamo Bay.“This is all whirling around us,” said Clayton G. Trivett Jr., the prosecutor, discussing key details of the negotiations in open court for the first time. He added that “around the edges we have agreed to do things” and that “the positions that we took at the time are still available.”In mostly secret negotiations in 2022 and 2023, prosecutors offered to drop the death penalty from the case in exchange for detailed admissions by the accused architect, Khalid Shaikh Mohammed, and four other men who are charged as his accomplices in the hijackings that killed nearly 3,000 people. Since then, one of the five men has been ruled not mentally competent to stand trial.The occasion of the briefing was a legal filing by lawyers for Ammar al-Baluchi, one of the defendants and Mr. Mohammed’s nephew, asking the judge to dismiss the case or at least the possibility of a death penalty because of real or apparent political interference by Senator Ted Cruz, Republican of Texas, and other members of Congress last summer.In August 2023, those members of Congress began urging relatives of Sept. 11 victims on social media to pressure President Biden to derail any deal that would prevent capital punishment.At the time, the White House was deciding whether to endorse certain conditions sought through the talks, most related to addressing the physical and psychological damage the men had from torture in their early years of incommunicado custody by the C.I.A.On Sept. 6, 2023, the White House declined to get involved.Rita J. Radostitz, a lawyer for Mr. Baluchi, said that Mr. Cruz then took “a victory lap.”“The Biden administration was prepared to give them a plea deal,” Mr. Cruz posted on social media. He went on, using the acronym for the Defense Department, “After I pressed the DoD, they reversed course & rejected the plea deal. Big win for justice.”But both defense and prosecution lawyers told the judge on Wednesday that the White House position did not derail the talks.When Mr. Cruz got involved, defense lawyers were “working with the prosecution streamlining all the litigation to present, in an open setting, a full examination of the events of 9/11 and answer all the victim family members’ questions about what happened,” said Gary D. Sowards, Mr. Mohammed’s lawyer.Any deal would take the death penalty off the table and require a mini-trial and airing of the facts of the attack, he said.The defendants want guarantees of trauma care for head injuries, gastrointestinal damage and mental illnesses blamed on their C.I.A. detention; to continue to eat and pray together communally, rather than be held in solitary confinement; and to get better communication with their families rather than recorded video calls. But Mr. Trivett said those demands, called “policy principles,” require infrastructure, funding and executive branch approval. So he forwarded them to the general counsel of the Defense Department while his team secretly negotiated how a plea agreement would play out in the Guantánamo court.He said Congress had legitimate interests in that aspect of the negotiations, because some assurances would require funding — and Congress decides the Pentagon’s budget.Mr. Sowards said a negotiated settlement at Guantánamo would not resemble one in federal court, where a defendant comes to plead guilty and is sentenced without a trial.These negotiations between prosecution and defense lawyers were working toward a lengthy, open court process that would involve a detailed plea, presentation of the crime, testimony by victims and possibly an opportunity for family members to have the defendants answer their questions, Mr. Sowards said.In military commissions, that process can last months.Mr. Trivett told the judge that about 20,000 people can be counted as relatives of the victims of the attacks, and there was no agreement “on what is justice in this case, what is an appropriate punishment.” He made the presentation on a rare week when only one relative was watching in the spectators’ gallery.“I’m glad to hear they’re still talking, and that there’s an openness to bringing a plausible resolution that will give some sort of finality to everyone involved,” said Colleen Kelly, whose brother Bill was killed at the World Trade Center.By “everyone,” she said, she meant the Sept. 11 families, the prosecution and the defense lawyers, some who have been shouldering this responsibility for two decades. Ms. Kelly, a founder of the Sept. 11th Families for Peaceful Tomorrows movement, came to Guantánamo on Saturday to watch a week of hearings as a court-approved “nongovernmental observer.”This is the third week of a five-week pretrial hearing session, and as it happened, the prosecutors sponsored no family members as guest observers.Last month, when family members were watching the proceedings, another prosecutor told the judge that, regardless of the outcome of their trial, Mr. Mohammed and the others could be held forever in a form of preventive detention.In disclosing the details of the continuing talks, Mr. Trivett said there had been no unlawful influence on his team. “Nobody has threatened me,” he said, adding that he was under no pressure “not to negotiate consistent with what we consider to be a just result.”On Wednesday, Darin Miller, a spokesman for Mr. Cruz, said the senator would continue his efforts.“During his time in the Senate, Senator Cruz has led efforts to combat terrorists, from the Iran-controlled Houthis to the Revolutionary Armed Forces of Colombia (FARC) to Hamas, in addition to advocating against plea deals for terrorists being charged for plotting and planning 9/11. He will continue to do so,” Mr. Miller said. More